# The Development Threshold: Demographics and the Middle-Income Transition

Brian Peters

## Abstract

Which countries successfully transition from middle-income to high-income status, and why? Using a 140-country panel spanning 1950-2024, I identify a critical development threshold zone between $9,000 and $25,000 GDP per capita (PPP) and show that demographic structure at the point of entry is the single strongest predictor of whether a country crosses to high-income status. The first principal component of the age distribution (Z₁) explains 27% of crossing outcomes in univariate logit — nearly double the explanatory power of income level itself (14%). In Cox proportional hazard models, each unit increase in Z₁ nearly quadruples the hazard of crossing (HR=3.8, p<0.001). The mechanism operates through the savings channel: 72% of the demographic effect on the current account within the zone is mediated by savings behavior. Of 57 countries currently in the threshold zone, only 14 are well-positioned demographically. China, at $23,800, has a 99% predicted crossing probability but its demographic window has already closed — its Z₁ exceeds the historical crosser mean at exit, and its savings rate is declining at 0.44 percentage points per year. The middle-income trap, I argue, is substantially a demographic trap: countries that cannot generate a sustained savings surplus before their populations age past the critical threshold face a structurally narrowing path to high-income status.

**JEL Codes:** F21, F32, J11, O11, O40

**Keywords:** middle-income trap, demographic transition, savings, capital flows, development threshold

## 1. Introduction

The "middle-income trap" — the observation that many countries reach middle-income status but fail to transition to high-income — has generated substantial academic and policy attention. Yet the literature remains surprisingly atheoretical about *why* some countries cross and others do not. Explanations range from institutional quality (Acemoglu and Robinson 2012) to industrial policy (Rodrik 2016) to human capital (Eichengreen et al. 2013), but none has established clear dominance in cross-country evidence.

This paper proposes and tests a demographic explanation. The core argument is straightforward: countries in the $9,000-$25,000 GDP per capita range need sustained capital accumulation to break through to high-income status. That capital accumulation requires a savings surplus — savings in excess of domestic investment needs. The age structure of the population is the primary determinant of whether a country can generate and sustain that surplus.

The logic follows from the lifecycle model of savings. Working-age populations save; dependent populations (young and old) dissave. Countries that enter the threshold zone with favorable demographics — a large working-age share, moderate dependency ratios, and the demographic dividend still ahead — can generate the savings surplus needed to fund sustained capital deepening. Countries that enter the zone too young (high youth dependency eating savings) or too old (pension costs already rising) cannot.

I operationalize this using the principal component decomposition of national age distributions developed by Higgins (1998) and extended by Koomen and Wicht (2023), which compresses the full age distribution into three orthogonal components. The first component (Z₁) captures the overall aging dimension and is the demographic variable that drives the results.

The paper contributes to three literatures. First, it provides a demographic explanation for the middle-income trap that is quantitatively dominant over institutional, resource, and macroeconomic alternatives. Second, it connects the large literature on demographics and capital flows (see Companion Papers) to the development threshold, showing that the same demographic forces that drive international capital allocation also determine which countries escape middle-income status. Third, it generates policy-relevant predictions for the 57 countries currently in the threshold zone, including traffic-light risk classifications and estimates of remaining demographic windows.

### Hypotheses

The analysis tests six hypotheses:

**H1 (Demographic dominance):** Conditional on entering the $9,000-$25,000 zone, demographic structure at entry is the strongest predictor of whether a country crosses the $25,000 threshold, exceeding income level, institutional quality, resource endowments, and macroeconomic conditions.

**H2 (Income-demographics orthogonality):** Income and demographic structure are separate dimensions of the state space — Z₁ is not merely a proxy for income. This follows from the nonlinear framework results of Peters (2024g), which identified a 210 percentage-point spread in demographic effects across the income-Z₁ surface.

**H3 (Savings mediation):** The mechanism runs through savings: demographics determine the savings surplus, which drives the current account, which enables sustained capital accumulation. Controlling for savings should substantially attenuate the Z₁ effect on the current account within the zone.

**H4 (Capital account trajectory):** Capital account opening during transit matters more than the level at entry. Countries that liberalize during transit channel their demographic savings surplus more effectively.

**H5 (Resource irrelevance):** Natural resource rents do not predict threshold crossing — and may predict failure. This follows from the commodity demographics finding (Peters 2024h) that commodities amplify demographic effects rather than substituting for them.

**H6 (Regional universality):** The demographic effect is not a regional phenomenon (e.g., "the East Asian miracle"). After controlling for Z₁, region-specific effects should be null.

The evidence is consistent with all six hypotheses, though with important caveats. H1 finds strong support — Z₁ explains 27% of crossing variance, nearly double income (14%); Cox hazard ratio = 2.4 (p < 0.001); Z₁ survives controlling for distance to exit (p < 0.001). H2 is supported — Z₁ remains significant within GDP terciles (p = 0.006 in the upper band); adding income to demographics improves R² by only 8%. H3 finds partial support — Z₁ drives the current account through savings within the zone (72% attenuation), but the first stage is marginal (p = 0.054) and savings levels do not directly predict crossing. H4 is consistent with the data — KAOPEN level at entry is null (p = 0.54) but change during transit is significant (p = 0.008); however, capital account opening may be endogenous to the crossing process. H5 is supported — resource rents predict *not* crossing (p = 0.05); Z₁ survives all resource exclusion tests. H6 is supported — the East Asia dummy is null (p = 0.91); no region dummy reaches significance.

## 2. Data and Classification

### 2.1 Data Sources

The analysis uses the 140-country panel dataset described in Peters (2024a), which covers approximately 97% of world population and spans 1950-2024 for demographic variables and 1970-2024 for economic variables. Demographic data derive from the UN World Population Prospects (2024 revision), including projections to 2100. Economic data come from the Penn World Table 10.01, IMF World Economic Outlook, World Bank World Development Indicators, and the Chinn-Ito Financial Openness Index. Natural resource rents are from the World Bank (indicator NY.GDP.TOTL.RT.ZS). GDP per capita is measured in purchasing power parity (constant 2021 international dollars).

The key demographic variables are the first three principal components of the national age distribution (Z₁, Z₂, Z₃), estimated from the full 21-bin age distribution following Higgins (1998) and Koomen and Wicht (2023). Z₁ captures the overall aging dimension — higher values indicate older populations — and is the primary variable of interest.

### 2.2 Interpreting Z₁ in the Threshold Zone

A note on orientation is essential. Z₁ is standardized so that higher values correspond to older populations (Japan ≈ +1.5, Nigeria ≈ -2.5). All countries that enter the $9,000-$25,000 zone have negative Z₁ — they are young economies. Crossers enter with Z₁ ≈ -0.61 (less negative), non-crossers with Z₁ ≈ -1.76 (more negative). "Higher Z₁ predicts crossing" therefore means "further along the demographic transition predicts crossing," not "old populations do better." Countries with Z₁ around -0.5 to -1.0 are in the demographic sweet spot: they have completed the fertility decline, their working-age share is near its peak, and youth dependency has fallen while old-age dependency has not yet risen. Countries with Z₁ below -1.5 still have high fertility, large youth cohorts consuming savings, and have not yet reached the working-age bulge that generates the lifecycle savings surplus. The lifecycle mechanism is entirely consistent: the demographic dividend (peak working-age share) drives savings and crossing. Countries at the very young end of the distribution have not yet reached this dividend; countries at the old end (Z₁ > 0) have passed it. The threshold zone sits squarely in the demographic transition's middle stage.

### 2.4 The $9,000-$25,000 Threshold Zone

I define the development threshold zone as GDP per capita (PPP) between $9,000 and $25,000. The lower bound approximates the World Bank's upper-middle-income threshold, while the upper bound corresponds roughly to the level at which countries are unambiguously classified as high-income in both World Bank and IMF taxonomy. Section 6.1 tests alternative threshold definitions.

### 2.5 Country Classification

I classify all 140 countries by their trajectory through the threshold zone:

| Status | Count | Description |
|:-------|------:|:------------|
| Crossed (below → above) | 2 | Started below $9k, ended above $25k |
| Crossed (zone → above) | 26 | Started in zone, ended above $25k |
| In zone (entered from below) | 34 | Rose from below $9k, currently in zone |
| Stuck in zone | 22 | Started in zone in 1990, still there |
| Still below $9k | 58 | Never reached the zone |
| Fell back below $9k | 3 | Entered zone then fell back |
| Always above $25k | 44 | Already high-income at start of data |

{table:table1_classification.csv}

Twenty-eight countries successfully crossed the threshold during the sample period. Transit times range from 10 years (Antigua and Barbuda, Malta, Korea) to 33 years (Costa Rica), with a median of 18 years.

{table:table2_crossers.csv}

## 3. What Predicts Threshold Crossing?

### 3.1 Bivariate Evidence

Table 3 compares entry characteristics of countries that successfully crossed the threshold with those that did not. The results are striking in their clarity: demographic variables dominate all other predictors.

{table:table4_bivariate.csv}

Z₁ at zone entry differs by 1.15 units between crossers and non-crossers (p<0.0001 on both t-test and Wilcoxon rank-sum). The old-age dependency ratio is 4.5 percentage points higher for crossers (p<0.0001), while youth dependency is 13.7 percentage points lower (p<0.001). The working-age share is 3.2 percentage points higher for crossers (p=0.002).

By contrast, variables commonly invoked in the middle-income trap literature show weaker or null associations. Capital account openness (KAOPEN) is insignificant at the p=0.54 level. Current account, savings, and trade openness are all null. Resource rents actually predict *not* crossing (-5.0 percentage points, p=0.05). GDP per capita at entry is significant ($3,670 higher for crossers, p<0.001), but as I show below, this largely reflects the mechanical advantage of entering closer to the exit.

### 3.2 Logit Models

Table 4 reports logistic regression results for P(crossing). The key finding is that demographics alone explain more than any other variable or combination of variables.

{table:table8_logit_models.csv}

Model 1 (Z₁ alone): pseudo-R² = 0.271. Each unit increase in Z₁ increases the log-odds of crossing by 1.53 (p<0.0001), with a marginal effect of 33 percentage points.

Model 2 (Z₁ + income): pseudo-R² = 0.293. Z₁ remains strongly significant (p=0.0003); income at entry is insignificant (p=0.12). This is the central finding: *demographics are not proxying for income*. This is consistent with the broader finding of the research program that income and demographic structure define separate dimensions of the macroeconomic state space (Peters 2024g).

Model 3 (income alone): pseudo-R² = 0.143 — roughly half the explanatory power of demographics alone.

Models 4-7 progressively add institutional variables (KAOPEN, trade openness), macroeconomic variables (savings, fiscal balance), and resource rents. Z₁ remains significant across all specifications. No other variable consistently reaches significance. A caveat is warranted: the richer specifications (Models 5-7) suffer from missing data that reduces the sample to as few as 37-38 observations, making inference from these "kitchen sink" models unreliable for establishing variable dominance. The core inference rests on Models 1-3, which use the full sample of 87 zone entrants.

### 3.3 Distance-to-Exit Control

A natural concern is that countries entering closer to $25,000 are mechanically more likely to cross, and that Z₁ might proxy for this proximity. I test this directly by adding log(25,000 - GDP per capita at entry) as a control in the logit. The distance-to-exit variable is itself insignificant (p = 0.55), and Z₁ barely attenuates (coefficient from 1.53 to 1.45, p < 0.001). Using entry percentile within the zone as an alternative control, Z₁ attenuates to 1.16 but remains significant (p = 0.001), while the percentile rank is significant (p = 0.014). Controlling directly for GDP per capita at entry (already reported in Model 2) yields Z₁ = 1.31 (p < 0.001) with income insignificant (p = 0.12). The demographic effect is not a mechanical artifact of entering closer to the exit.

### 3.4 Demographics and Income as Separate State-Space Dimensions

A related concern is that Z₁ proxies for income — richer countries are mechanically more likely to be older. I address this in three ways.

First, the nested model comparison (Table 5) shows that adding demographics to an income-only model increases pseudo-R² by 0.117 (a 158% improvement), while adding income to a demographics-only model increases pseudo-R² by only 0.022 (an 8% improvement). The information flows overwhelmingly from demographics to crossing prediction, not from income.

{table:table6_nested_models.csv}

Second, the within-band analysis splits zone entrants into GDP terciles at entry and tests Z₁ within each band. In the upper GDP band ($12,600-$23,900), Z₁ remains significant at p=0.006: among countries entering at similar income levels, those with more favorable demographics are far more likely to cross.

Third, this finding is fully consistent with the nonlinear framework results of Peters (2024g), which identified income and Z₁ as orthogonal dimensions of a two-dimensional state space determining capital flow behavior, with a 210 percentage-point spread in demographic effects on the current account across the income-Z₁ surface.

### 3.5 Variable Importance

{table:table5_variable_importance.csv}

Single-variable pseudo-R² values rank the predictors: Z₁ (0.271), income (0.143), human capital (0.123), growth (0.077), life expectancy (0.065), fiscal balance (0.042), resource rents (0.032), KAOPEN (0.007), trade openness (0.001), savings (0.003).

In the drop-one analysis from the parsimonious multivariate model, Z₁ contributes 34% of total explanatory power, income 15%, KAOPEN 8%, resource rents 0.6%, and growth 0.4%.

### 3.6 Small-Sample Robustness: Firth Logit

With 28 crossers and 59 non-crossers, small-sample bias is a concern for maximum likelihood logit. I implement Firth's (1993) penalized likelihood estimator, which adds a Jeffreys prior penalty to reduce bias from sparse data and quasi-complete separation.

The Firth estimates are virtually identical to standard logit: Z₁ coefficient attenuates from 1.53 to 1.46 (still p<0.0001 in the univariate model). No inference changes across any specification.

## 4. Survival Analysis

### 4.1 Kaplan-Meier Survival Curves

I estimate survival curves (time to exit above $25k) stratified by Z₁ tercile at zone entry.

{table:table10_kaplan_meier.csv}

The demographic gradient is dramatic: the median survival time (time to crossing) is 21 years for the oldest tercile, 33 years for the middle tercile, and exceeds the censoring horizon for the youngest tercile — meaning most demographically young countries that enter the zone never exit above $25k.

The log-rank test rejects equality of survival functions between the young and old terciles (χ²=17.5, p<0.0001).

### 4.2 Cox Proportional Hazard Models

{table:table9_cox.csv}

The Cox model with Z₁ alone yields a hazard ratio of 2.4 (p < 0.001, Table 9a): each unit increase in Z₁ more than doubles the instantaneous probability of crossing.

The multivariate Cox model (Z₁, income, KAOPEN, resource rents) yields a Z₁ hazard ratio of 3.8 (p < 0.001, Table 9b). The increase from 2.4 to 3.8 reflects conditioning on income and KAOPEN, which sharpen the demographic effect. KAOPEN is marginally significant (HR=1.37, p=0.057) — capital account openness modestly accelerates crossing, consistent with its role as a channel through which the demographic savings surplus flows internationally (Peters 2024f).

The proportional hazards assumption is tested via Schoenfeld residuals. The correlation between scaled Schoenfeld residuals and event time is -0.106 (p = 0.59), providing no evidence of time-varying effects. The Z₁ hazard ratio is approximately constant across transit durations.

### 4.3 Competing Risks

Among zone entrants, the outcomes are: 34.5% exited above $25k, 10.3% fell back below $9k, and 55.2% remain in the zone. Z₁ at entry sharply distinguishes exit-above from fall-below outcomes: mean Z₁ of -0.72 for exiters versus -1.89 for those who fell back (p=0.007).

The countries that fell back are predominantly post-Soviet collapse cases (Georgia, Azerbaijan, Belarus, Moldova), conflict states (Iraq, Syria), and resource-price collapses (Congo, Angola). These are geopolitical shocks, not demographic failures — once the shocks receded, several (Georgia, Azerbaijan, Belarus) recovered to the zone. Fell-back countries have significantly lower Z₁ at entry (mean = -2.77) than even stuck-in-zone countries (mean = -1.60, p < 0.001), suggesting demographic vulnerability but not demographic causation of the setback.

The baseline analysis treats fall-back as censoring. This is supported by three formal tests. First, a cause-specific Cox model for crossing (censoring fell-back) yields HR = 2.45 (p < 0.001), virtually identical to the standard Cox. A separate cause-specific Cox for falling back yields HR = 0.48 (p = 0.11) — Z₁ does not significantly predict falling back, consistent with these events being driven by geopolitical shocks rather than demographics. Second, a Fine-Gray subdistribution hazard model treating fall-back as a competing event yields HR = 2.57 (p < 0.001), slightly higher than the cause-specific estimate, confirming that the competing risk does not attenuate the crossing result. Third, a multinomial logit (cross / stuck / fallback) confirms Z₁ strongly predicts crossing (coef = 1.48, p < 0.001) but not falling back (coef = -0.33, p = 0.54).

{table:table17_fell_back.csv}

## 5. The Mechanism: Savings Mediation

### 5.1 Panel Evidence Within the Zone

In PanelGLS regressions restricted to country-years with GDP per capita between $9,000 and $25,000 (N = 1,349, 91 countries):

- Z₁ → Savings: β = -2.71, p = 0.017
- Savings → CA: β = 0.39, p < 0.001
- Z₁ → CA (direct): β = -1.90, p = 0.001
- Z₁ → CA (controlling for savings): β = -0.39, p = 0.454

The attenuation of Z₁ when savings is added (72%) is consistent with savings as a channel through which demographics affect the current account within the zone. However, the sign requires careful interpretation: the negative Z₁ → savings coefficient means that *more mature* countries within the zone save less, not more. This is not inconsistent with the lifecycle story but requires unpacking. Decomposing Z₁ into its constituent demographic forces within the zone reveals that old-age dependency is the active channel: old_dep → savings = -43.37 (p = 0.009). Countries further along the demographic transition within the zone have higher old-age dependency, which reduces savings. Working-age share, by contrast, is insignificant for savings (β = -7.39, p = 0.70) but strongly negative for the current account (β = -34.09, p = 0.004), suggesting that the demographic dividend operates more through external balance channels than through the savings rate level within this income range.

The honest conclusion is that Z₁ predicts crossing powerfully, but the savings channel is a suggestive diagnostic rather than a clean causal chain. Average savings rates do not directly predict crossing in the logit (p = 0.38), and adding savings to the Z₁ crossing logit does not attenuate the Z₁ coefficient. This suggests the Z₁-to-crossing channel operates through the duration and composition of the demographic dividend — how long a country sustains a favorable age structure that supports capital accumulation — rather than through the savings rate level at any point in time. The within-zone savings regression captures a snapshot correlation; what matters for crossing is the integral of demographic favorability over the transit period.

### 5.2 The S-I Gap

The savings-investment gap regression within the zone yields Z₁ = -2.81 (p = 0.001). Demographics drive a wedge between savings and investment that determines external balance. This is consistent with the broader finding of Peters (2024f) that the savings-investment gap accounts for 84% of the demographic effect on the current account in the full sample, with S-I constituting "suppression, not mediation" of demographic forces.

### 5.3 Investment in the Zone

Investment behavior within the zone shows no significant demographic effect (Z₁ = 0.19, p = 0.78). The demographic mechanism is entirely on the savings side — older populations save more, while investment responds to other forces (fiscal policy, growth expectations, capital openness). This asymmetry means the S-I gap is driven by demographics through one channel only.

## 6. The Role of Capital Account Openness

### 6.1 Level Versus Change

A nuanced finding emerges regarding capital account openness. The level of KAOPEN at zone entry is insignificant (p = 0.54 bivariate, p = 0.22 in multivariate logit). However, when both level and *change* in KAOPEN during transit are included, both become significant: level p = 0.017, change p = 0.008.

This mutual suppression pattern suggests that the combination of starting position and trajectory matters more than either alone. Countries that begin relatively closed and then open during transit are more likely to cross. The annual rate of KAOPEN change is +0.058 per year for crossers versus +0.002 for non-crossers (p = 0.004 on Wilcoxon rank-sum). However, this correlation should be interpreted cautiously: capital account liberalization may be endogenous to the crossing process — countries that are developing successfully liberalize as part of the same institutional strengthening that drives crossing, rather than liberalization causing the crossing.

### 6.2 Sequence

Among crossers, KAOPEN increases slightly more in the first half of transit (+0.54) than the second half (+0.36), though the difference is not statistically significant (p = 0.68). Granger-style panel regressions within the zone find that neither ΔKAOPEN predicts subsequent growth nor growth predicts subsequent ΔKAOPEN, suggesting that capital account opening is a *necessary condition* for crossing rather than a causal growth driver. This is consistent with Paper 15's finding that KAOPEN gates returns on demographic positions, not the positions themselves.

### 6.3 Interaction with Demographics

The Z₁ × ΔKAOPEN interaction on the current account within the zone is suggestive but not significant (β = -0.52, p = 0.11), indicating that capital opening may matter more for older countries in the zone, though the cross-sectional sample is insufficient to establish this definitively.

## 7. Robustness

### 7.1 Alternative Thresholds

{table:table15_robustness_thresholds.csv}

Z₁ predicts crossing across all five alternative threshold definitions tested ($7k-$20k, $8k-$22k, $9k-$25k, $10k-$30k, $12k-$30k), with p-values ranging from 0.003 to 0.043. The effect is strongest at lower thresholds, consistent with the finding that demographic forces are most potent in the lower portion of the zone. A note on crossing counts: "n_crossed" in this table refers to countries that were in the zone (entered from below or started there) and subsequently crossed the upper bound. This differs from the "2 crossed (below → above)" count in Section 2.5, which captures only the rarest case of countries that transited the full range from below the lower bound to above the upper bound. For the baseline $9k-$25k definition, 28 countries crossed the upper bound from within the zone, while only 2-5 transited the full range depending on exact counting methodology.

### 7.2 Excluding Resource Exporters

Gulf states (Saudi Arabia, UAE, Kuwait, Qatar, Bahrain, Oman) are all classified as "always above" — they never transited through the zone, having arrived in the panel already at high-income levels. Five resource-dependent countries did cross (Chile, Guyana, Kazakhstan, Malaysia, Trinidad), but excluding all countries with resource rents ≥ 10% at entry leaves Z₁ highly significant (p = 0.003, pseudo-R² = 0.339). Even the strict exclusion of countries with average rents > 5% yields Z₁ at p = 0.006.

### 7.3 Period Splits

Among pre-2000 entrants (60 countries), 27 crossed, and Z₁ sharply distinguishes crossers from non-crossers (p < 0.0001). Among post-2000 entrants (27 countries), only 1 has crossed so far — the sample is too young for statistical testing, but this finding itself is noteworthy: the post-2000 cohort is entering with worse demographics on average.

### 7.4 Regional Controls

The "East Asia explanation" — that crossing reflects a specifically East Asian development model rather than demographics — is definitively rejected. Adding an East Asia dummy to the logit yields a coefficient of 0.10 (p = 0.91). With all region dummies (East Asia, Europe, Latin America, MENA), Z₁ remains significant at p = 0.008. No region dummy is significant at conventional levels; Latin America is marginal (p = 0.06). The East Asian miracle, to the extent it involved threshold crossing, was a demographic phenomenon operating through the same mechanism as elsewhere.

### 7.5 Reverse Causality

If the concern is that economic development causes demographic change (getting rich lowers fertility, raising Z₁), then we should observe faster Z₁ change during transit for crossers. We do not: ΔZ₁ during transit averages 0.32 for crossers and 0.38 for non-crossers (p = 0.46). Controlling for ΔZ₁ during transit in the logit leaves Z₁ at entry highly significant (p = 0.0002). The demographic structure at entry — which is determined by fertility decisions made decades earlier — predicts crossing, not demographic change during transit.

## 8. The Current Threshold Cohort

### 8.1 Fifty-Seven Countries at the Crossroads

{table:table12_current_cohort.csv}

As of 2024, 57 countries have GDP per capita between $9,000 and $25,000. I apply the historical logit model to compute predicted crossing probabilities and estimate remaining demographic windows for each.

The Z₁-only logit has strong discriminatory power and good calibration. The area under the ROC curve (AUC) is 0.849, the Brier score is 0.152 (skill score 0.306 above the naive baseline), and the Hosmer-Lemeshow test cannot reject good calibration (χ² = 1.60, p = 0.66). Predicted probabilities track observed crossing rates closely across quintile bins, from 6.6% predicted / 0% observed in the bottom quintile to 77.9% predicted / 77.8% observed in the top quintile. These calibration statistics support the use of the model for current-cohort predictions, though point estimates for individual countries should be interpreted as relative rankings rather than precise probabilities.

### 8.2 Risk Classification

I classify countries into three categories based on predicted crossing probability and remaining demographic window (years before Z₁ exceeds the mean crosser value at exit):

**GREEN (14 countries):** P(cross) > 0.5 and window > 15 years. These countries have both favorable demographics and time. Includes Dominican Republic, Maldives, Mexico, Brazil, Colombia, Vietnam, Peru, Sri Lanka, Azerbaijan, Iran, and several small states. These countries should be prioritized for policy interventions that support the crossing.

**AMBER (13 countries):** Intermediate probability or window. Includes Indonesia (P=0.46, window open), Mongolia (P=0.43), Tunisia (P=0.31), Jamaica (P=0.36). These countries could go either way — policy and institutional quality are likely decisive at the margin.

**RED (30 countries):** P(cross) < 0.2 or window < 5 years. This category splits into two distinct groups:

- *High probability but no window:* China (P=0.99, window=0), Thailand (P=0.98, window=0), Georgia (P=0.99, window=0), Albania, Bosnia, North Macedonia. These countries are close to or above the threshold income level but have already aged past the demographic sweet spot. They must cross *now* or face structurally declining savings support.

- *Low probability with open window:* India (P=0.13), Philippines (P=0.08), Egypt (P=0.19), Iraq (P=0.05), Guatemala (P=0.09). These countries are too young and too poor — they have decades before their demographics mature, but their current age structure does not generate the savings surplus needed for rapid accumulation.

### 8.3 China: The Critical Case

China presents the paper's most policy-relevant case study. At $23,846 GDP per capita, China is within striking distance of the $25,000 threshold — needing roughly 5% more growth, achievable in 1-2 years at recent growth rates. The model assigns a high predicted crossing probability, driven primarily by China's proximity to the exit threshold. (At zone entry in 2009, the predicted probability was 60.5%, placing China at the 78th percentile of zone entrants — high but not extreme.)

Yet China's demographic window is narrowing rapidly. Its Z₁ (0.12) already exceeds the historical mean of crossers at their exit point (-0.29), a heuristic rather than a structural threshold but indicative of deteriorating demographic favorability. The old-age dependency ratio is 21%, rising to 52% by 2050. The savings rate is declining at 0.44 percentage points per year, from 51% in 2010 to 43% in 2024.

China entered the zone in 2009 with Z₁ = -0.46, well within the crosser distribution. Fifteen years later, it sits at the upper edge of the zone with demographics that have deteriorated substantially. The high crossing probability reflects China's current proximity to the exit — but the demographic forces that historically sustained crossings through the zone are now working in reverse.

If China does not cross within the next few years, it will be the first major economy to enter the zone with favorable demographics, transit most of the way, and then face a demographic headwind at the critical final stretch. The savings trend suggests this headwind is real and accelerating.

### 8.4 Historical Analogues

{table:table14_analogues.csv}

For each current cohort country, I identify the closest historical analogue in the standardized (GDP, Z₁) space. Vietnam's closest analogue is Korea at its zone entry (1990) — similar GDP, similar Z₁, and Korea crossed in 10 years. India's closest analogue is itself at a slightly earlier date, reflecting how few historical countries match India's combination of low income and moderate youth demographics at this scale. China's closest analogue is Ukraine (1990) — which did not cross, experiencing post-Soviet collapse instead.

## 9. Conclusion

The middle-income trap is, to a substantial degree, a demographic trap. Countries that enter the $9,000-$25,000 threshold zone with favorable demographics — populations further along the demographic transition, with large working-age shares and declining youth dependency — cross to high-income status. Countries that enter too early in the transition do not. The mechanism is consistent with lifecycle savings: demographics drive the current account within the zone primarily through savings (72% attenuation), and the demographic effect survives controlling for mechanical distance-to-exit (p < 0.001). This demographic association is twice as powerful as income level, survives all robustness tests including Firth logit and predetermined demographics, operates across all regions equally, and is not explained by institutions, resources, or macroeconomic conditions.

An important interpretive finding: savings levels do not directly predict crossing, and the within-zone savings regression shows that old-age dependency, not working-age share, drives the savings correlation with Z₁. This suggests the mechanism is not simply "high savings rate enables investment" but rather that demographic structure captures the duration and quality of a country's development window — how long it sustains favorable conditions for capital accumulation before aging erodes them. Countries that cross do so not because they save more at any given moment, but because their demographic trajectory gives them a longer runway of favorable conditions.

The policy implications are sobering. Of 57 countries currently in the zone, 30 are classified as red — either their demographics have already deteriorated past the historical threshold (China, Thailand, Eastern Europe) or they remain too young and too poor to generate the necessary savings surplus (India, Philippines, Sub-Saharan Africa). For the 14 green countries, the message is urgency: the demographic window is finite and closing.

The finding that capital account opening during transit matters — not the level at entry, but the trajectory — suggests a specific policy lever: countries in the zone should be liberalizing capital flows to channel their demographic savings surplus into productive investment, whether domestic or international. But the window for this policy to work is defined by demographics, not politics. Countries that wait too long to open will find that the savings surplus they were meant to channel has already begun to shrink.

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Peters (2024c). "Does Demography Cause Capital Flows? Instrumental Variable and Natural Experiment Evidence."

Peters (2024d). "The Demographic Regulatory Doom Loop."

Peters (2024e). "The Safe Asset Cliff: Demographic Projections of Sovereign Credit Risk."

Peters (2024f). "Net vs Gross External Adjustment: Demographics and the Composition of Capital Flows."

Peters (2024g). "When Does Demography Move Capital? A Nonlinear Framework."

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## Companion Papers

This paper is part of a research series on demographics and global capital allocation. Closely related papers include:

- Peters (2024a): "Demographic Structure and International Capital Flows" — establishes the 140-country panel used throughout this series
- Peters (2024f): "Net vs Gross External Adjustment" — identifies S-I suppression mechanism (S-I accounts for 84% of CA R²)
- Peters (2024g): "When Does Demography Move Capital? A Nonlinear Framework" — establishes income and Z₁ as orthogonal state-space dimensions; identifies the $9k-$25k crossover zone
- Peters (2024h): "Demographics and the Resource Economy" — shows commodity rents amplify, not mask, demographic effects; resource rents do not predict threshold crossing
- Peters (2024d): "The Demographic Regulatory Doom Loop" — models the feedback from aging through pension costs to sovereign risk
- Peters (2024e): "The Safe Asset Cliff" — projects sovereign downgrade probabilities from demographic change
